where n^ is the nth moment of the spectral density 



n^ = / S n (f) f n df (6) 



o 



A more detailed discussion on the analysis can be found in Reference 17. 



The RMS spreading angle for a narrow banded sea can be determined by: 



^ (T) 



8 p = [2 - 2( ai 2 + b^) 1 ^] 



DATA PROCESSING 



The Wave-Track data was passed through a two hertz low pass filter and digi- 

 tized at four samples per second per channel. The tape speed was set at 3—3/ U ips. 

 This is equivalent to an actual sample rate of two hertz with a low pass filter 

 cutoff at one hertz. The engineering units are applied to the data, while the data 

 in the direction channels are converted from tilt angles to slopes. When 

 necessary, the data were filtered using a two-pole high pass filter to eliminate 

 electronic drifts or offsets. The auto and cross spectra were calculated using a 

 Fast Fourier Transformation (FFT) . The data runs were divided into segments, each 

 of a size based on the power of two. A cosine window was applied to each segment 

 and the segments are overlapped by 50 percent. 



The real and the imaginary parts of the cross spectra of each of the three 

 channels were calculated to give the coincident and the quadrature spectra. From 

 these, the Fourier coefficients were calculated, along with the directions, 

 periods, and energies. 



Typical lengths of a run are 1728 and 1600 seconds with the number of degrees 

 of freedom of 51 and k'J , respectively. 



DISCUSSION 



The data presented here represent two different approaches to measuring 

 waves and their directions from a ship launched buoy. Delft University analyzed 

 the WAVEC data and reported them in Reference 9. DTNSRDC analyzed the Wave-Track 

 data. 



The displayed results for a comparison of the two buoys include time histories 

 of significant wave height, modal wave period, and mean wave directions. In the 



